% Simplified version of an UMTYMP template.
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% If the text is too small, change 10pt to 12pt
\documentclass[10pt]{article}
\RequirePackage{amsmath,amsthm,amssymb,latexsym,amsthm,verbatim,xspace,amstext,xspace,setspace}
% Here's where you edit the class, section and title information
\newcommand{\headerclass}{UMTYMP Calculus III}
\newcommand{\headersection}{Colley 2.3}
\newcommand{\headertitle}{Partially Practicing}
% Set a fixed margin along all sides
\usepackage[margin=.75in, nohead, pdftex]{geometry}
% Re-adjust the top margin if desired
\topmargin -0.2in
% These packages used for spacing in the header and throughout
% This next command affects the page numbering. "empty" is best for short handouts
\pagestyle{empty}
% Uncomment one of the following to set the spacing to single, 1.5 or double spacing
%\singlespacing
\onehalfspacing
%\doublespacing
% This prevents paragraphs from begin indented. Comment it out to have indentation.
\parindent 0ex
% Finally we start!
\begin{document}
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% This is the "header" at the top. You shouldn't have to edit these lines!
% Instead, chance the Class, Section and Title above.
\headerclass\xspace \hspace{\stretch{1}} \headersection
\begin{center}{ \large \textbf{\headertitle} }\end{center}
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% At this point, you might have some introductory text, or jump straight
% into an ``enumerate'' environment for the problem statements.
\begin{enumerate}
\item Compute the partial derivatives of the following function.
\begin{enumerate}
\item $\displaystyle f(x,y)=3x^{5}y - x^{2}y^{2}$
\vspace{1.5in}
\item $\displaystyle g(x,y)=\arctan{(y \sqrt{x})}$
\vspace{1.5in}
\end{enumerate}
\item Consider the function $\displaystyle f(x,y) = \begin{cases} \frac{x^3-y^3}{x^2+y^2}, & (x,y)\ne (0,0)\\ 0 & (x,y)=(0,0) \end{cases}$.
\begin{enumerate}
\item Explain why you cannot use the quotient rule to compute $f_x (0,0)$.
\vspace{1in}
\item Compute $f_x (0,0)$ using the limit definition.
\end{enumerate}
\end{enumerate}
\end{document}